广义Hadwiger数的渐近性
Asymptotics of generalized Hadwiger numbers
摘要：
本文给出了中心对称椭圆$B$与具有可求长边界的二维区域$F$有公共点的非重叠位似拷贝数的渐近估计，推广了L.Fejes-Toth，K.Borockzy Jr.，D.G.Larman、S.Sezgin、C.Zong和作者。渐近式计算由$B$确定的Minkowski度量中的边界$\partial F$的长度。证明的核心包括一个方法，用于沿着闵可夫斯基平面中具有正到达的曲线滑动凸珠。我们还证明了水平集是可求长的子集，并将Erdös，Oleksiv和Pesin关于欧几里得空间的一个定理推广到Minkowski空间。
英文摘要：
We give asymptotic estimates for the number of non-overlapping homothetic copies of some centrally symmetric oval $B$ which have a common point with a 2-dimensional domain $F$ having rectifiable boundary, extending previous work of the L.Fejes-Toth, K.Borockzy Jr., D.G.Larman, S.Sezgin, C.Zong and the authors. The asymptotics compute the length of the boundary $\partial F$ in the Minkowski metric determined by $B$. The core of the proof consists of a method for sliding convex beads along curves with positive reach in the Minkowski plane. We also prove that level sets are rectifiable subsets, extending a theorem of Erdös, Oleksiv and Pesin for the Euclidean space to the Minkowski space.
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